Magnetic Resonance Imaging (MRI), or nuclear magnetic resonance imaging, is commonly used to visualize detailed internal structures in the body. MRI provides superior contrast between the different soft tissues of the body when compared to x-ray computed tomography (CT). Unlike CT, MRI involves no ionizing radiation because it uses a powerful magnetic field to align protons, most commonly those of the hydrogen atoms of the water present in tissue. A radio frequency electromagnetic field is then briefly turned on, causing the protons to alter their alignment relative to the field. When this field is turned off the protons return to their original magnetization alignment. These alignment changes create signals that are detected by a scanner. Images can be created because the protons in different tissues return to their equilibrium state at different rates. By altering the parameters on the scanner this effect can be used to create contrast between different types of body tissue. MRI may be used to image every part of the body, and is particularly useful for neurological conditions, for disorders of the muscles and joints, for evaluating tumors, and for showing abnormalities in the heart and blood vessels. Magnetic resonance imaging (MRI) methods provide several tissue contrast mechanisms that can be used to assess the micro- and macrostructure of living tissue in both health and disease. Diffusion MRI is a method that produces in vivo images of biological tissues weighted with the local microstructural characteristics of water diffusion. There are two distinct forms of diffusion MRI, diffusion weighted MRI and diffusion tensor MRI. In diffusion weighted imaging (DWI), each image voxel (three-dimensional pixel) has an image intensity that reflects a single best measurement of the rate of water diffusion at that location. This measurement is more sensitive to early changes such as occur after a stroke than more traditional MRI measurements such as T1 or T2 relaxation rates. DWI is most applicable when the tissue of interest is dominated by isotropic water movement, e.g., grey matter in the cerebral cortex and major brain nuclei—where the diffusion rate appears to be the same when measured along any axis. Traditionally, in diffusion-weighted imaging (DWI), three gradient-directions are applied, sufficient to estimate the trace of the diffusion tensor or ‘average diffusivity’, a putative measure of edema. Clinically, trace-weighted images have proven to be very useful to diagnose vascular strokes in the brain, by early detection (within a couple of minutes) of the hypoxic edema.
Diffusion tensor imaging (DTI) is a technique that enables the measurement of the restricted diffusion of water in tissue in order to produce neural tract images instead of using this data solely for the purpose of assigning contrast or colors to pixels in a cross sectional image. It also provides useful structural information about muscle—including heart muscle, as well as other tissues such as the prostate. DTI is important when a tissue—such as the neural axons of white matter in the brain or muscle fibers in the heart—has an internal fibrous structure analogous to the anisotropy of some crystals. Water tends to diffuse more rapidly in the direction aligned with the internal structure, and more slowly as it moves transverse to the preferred direction. This also means that the measured rate of diffusion will differ depending on the position of the observer. In DTI, each voxel can have one or more pairs of parameters: a rate of diffusion and a preferred direction of diffusion, described in terms of three dimensional space, for which that parameter is valid. The properties of each voxel of a single DTI image may be calculated by vector or tensor math from six or more different diffusion weighted acquisitions, each obtained with a different orientation of the diffusion sensitizing gradients. In some methods, hundreds of measurements—each making up a complete image—can be used to generate a single resulting calculated image data set. The higher information content of a DTI voxel makes it extremely sensitive to subtle pathology in the brain. In addition, the directional information can be exploited at a higher level of structure to select and follow neural tracts through the brain—a process called tractography.
Tractography is the only available tool for identifying and measuring pathways in the brain (neural tracts) non-invasively and in-vivo. By comparison with invasive techniques, tractography measurements are indirect, difficult to interpret quantitatively, and error-prone. However, their non-invasive nature and ease of measurement mean that tractography studies can address scientific questions that cannot be answered by any other means. In particular, brain connections can be measured in living human subjects, and measurements can be made simultaneously across the entire brain. Hence, areal connections may be compared in humans across many cortical and sub-cortical sites. Furthermore, connections can be compared with other in-vivo measures such as functional connectivity and behavior across individuals.
More extended diffusion tensor imaging (DTI) scans derive neural tract directional information from the data using 3D or multidimensional vector algorithms based on three, six, or more gradient directions, sufficient to compute the diffusion tensor. The diffusion model is a rather simple model of the diffusion process, assuming homogeneity and linearity of the diffusion within each image voxel. From the diffusion tensor, diffusion anisotropy measures such as the fractional anisotropy (FA) can be computed. The principal direction of the diffusion tensor can be used to infer the white-matter connectivity of the brain. Recently, more advanced models of the diffusion process have been proposed to overcome the weaknesses of the diffusion tensor model. Amongst others, these include q-space imaging and generalized diffusion tensor imaging.
Reconstruction of tissue fiber pathways from volumetric diffusion weighted magnetic resonance imaging (DW-MRI) data is an inherently ill-posed problem because the local (voxel) diffusion measurements are noisy and made on a scale significantly greater than the underlying fibers and, thus, there are a multitude of possible neural pathways between any two given points in the imaging volume that might be consistent with the experimental data. The question then is to find the paths that are most probable. Current fiber tractography methods generally fall into two categories: 1) deterministic methods, typically based on some form of streamline construction, probabilistic methods, also generally based on streamline construction, but with the most likely principal diffusion direction determined from a posterior distribution of principal diffusion directions. These algorithms are “local” in the sense that the computations are done at each voxel and some small neighborhood around it and thus are not informed by the final path that is created, and thus are not capable of assessing the probability of the final path amongst all possible paths. In most cases, these algorithms are inherently based upon some underlying relation to a random walk which guides the evolution of the trajectories.
Recently, interest has grown in more “global” methods that take into account the probabilities of the final paths by incorporating the path probabilities into the estimation process. These methods are typically based upon parameterizations of the diffusion field, or the anatomical connections they imply, that extend spatially beyond the voxel dimensions and subsequently take the form of either improving the local computations by the incorporation of more spatially extended path lengths or on the extremization of a cost function over a multitude of possible paths. These global methods usually (with some exceptions do not take the random walk viewpoint but rather view the entire system as possessing some underlying structure, characterized by local interactions or potentials, that can be elucidated by optimizing some cost function (e.g., energy) over multiple configurations of that system.
The original diffusion tensor imaging (DTI) model assumes that the measurements in each voxel provide an estimate of a single real, 3×3 symmetric diffusion tensor D from whose eigenstructure can be derived both a meaningful measure of the anisotropy (here characterized by the fractional anisotropy FA and a principal eigenvector that can be used as a proxy for the fiber orientation. Then DTI is the simplest underlying model for diffusion tensor data, is predicated on a single fiber model for the voxel content, and is equivalent to a Gaussian model for diffusion. However, the DTI model is not sufficient to capture more realistic possibilities of complex fiber crossings needed for clinical applications. To estimate local diffusion directions in each voxel (streamline directions) several high angular resolution diffusion imaging (HARDI) methods are typically used. These methods represent an extension of the original DTI method to higher angular resolutions appropriate not only for detection of main fiber orientation, but also for attempting to resolve more complex intravoxel fiber architecture such as multiple crossing fibers.
In recent years, there has been significant interest in developing DW-MRI methods capable not only of estimating angular fiber distributions from multidirectional diffusion imaging (multiple q-angles), but also find spatial scales with multiple diffusion weightings (multiple b-shells). While it has long been recognized that the most general nonparametric (model-free) approach is to measure the displacement probability density function or diffusion propagator directly, the natural extension of this to imaging wherein 3D Cartesian sampling of q-space is used to obtain the 3D displacement probability density function (dPDF) at each voxel, is prohibitively expensive from the standpoint of data acquisition. This recognition has recently spawned more practical methods for obtaining an estimate of the dPDF, often called the ensemble average propagator (EAP), from more practical multi-shell, multi-directional acquisitions. See, e.g., Merlet, et al., “TRactography via the Ensemble Average Propagator in diffusion MRI”
Despite these advances, a critical simplification that is made in all current methods used to estimate either the intravoxel diffusion characteristics (via the EAP, for example) or to estimate the underlying global structure (tractography) is the assumption that these two estimation procedures are independent. Thus, one must first estimate the intravoxel diffusion, then apply a tractography algorithm. For example, multiple b-shell effects, used in obtaining the EAP, are used only to infer directional multiple fiber information for input into streamline tractography algorithms. However, this distinction between local and global estimation is artificial and limiting, since both the local (voxel EAP) information and the global structure (tracts) are from the same tissue, just seen at different scales.